Fast half-quadratic algorithm for image restoration and reconstruction

lp−lq problems with 0 < p, q ≤ 2 have received significant attentions in image restoration and compressive sensing. Half-quadratic regularization method is usually a technique to solve this problem. To improve the performance of this technique, instead of conjugate gradient(CG) method, we propose an alternating direction method of multipliers (ADMM) as the inner iterations to solve the corresponding linear equations. The convergence of the resulting algorithm is discussed. Numerical results related to some image restoration and reconstruction problems are presented to demonstrate the effectiveness of our method.